Formal Formality of the Hypercommutative Algebras of Low Dimensional Calabi-Yau Varieties

Abstract

There is a homotopy hypercommutative algebra structure on the cohomology of a Calabi-Yau variety. The truncation of this homotopy hypercommutative algebra to a strict hypercommutative algebra is well-known as a mathematical realization of the genus zero B-model. It is shown that this truncation loses no information for some cases, including all Calabi-Yau 3-folds. © 2014 Springer-Verlag Berlin Heidelberg.